In recent years sigma delta converters of the low-pass type have been used successfully in A/D or D/A converters, but they are also used in different types of Class-D amplifiers. Further, band-pass sigma delta converters have been used successfully for frequency up/down modulation in combination with digital or analogue conversion of RF base-band signals used in digital wireless communications system.
Conventional converters are build around a quantizer with a relatively fine resolution typically specified by the number of bits with which the signal is represented e.g. 8 bits, 12 bits or 16 bits. However, due to the fine resolution quantizer they are relatively complex in structure compared to the sigma delta converter. Further improvements of the conventional converter are cumbersome in that, on the one hand, further improvements of the fine resolution of the conventional converters will cause a dramatic increase in the complexity of the converter. Additionally, expensive matching or trimming of components is required. On the other hand, an increased sampling frequency will in general add extra costs to the manufacture of the converter. Conventional converters sample an input signal at the Nyquest frequency, however, over-sampling of typically two to 16 times may be applied.
Sigma delta converters are less complex in their basic structure than the conventional converters. They are built around a quantizer with a relatively coarse resolution of typically 2, 3 or 4 levels of the full scale input signal. This low resolution quantizer can be operated at a greater sampling frequency than the fine resolution quantizer, but at the cost of a larger quantization error i.e. the difference between the input signal and the output signal.
To compensate for the larger quantization error, the sigma delta modulator is configured with a feedback loop where the integral of the quantization error modulates the quantizer. Further, the sigma delta modulator operates with relatively high over-sampling ratios of e.g. 32, 50, 64 or 128 times. The signal to the sigma delta modulator is typically sampled at the over-sampled sampling frequency which is also denoted the clock frequency of the sigma delta modulator. The sigma delta modulator operates at this clock frequency equal to the over-sampling ratio multiplied by the sampling frequency. By means of the configuration and the high clock frequency the quantization error is integrated at the relatively high clock frequency, typically multitudes above the Nyquest frequency, to provide a signal which in average, across a Nyquest sampling time interval, has almost no error. A typical clock frequency for audio band signal processing is e.g. 1.2 MHz or 2.4 MHz.
A bit stream at the greater sampling frequency is generated. Since typically it is inconvenient to perform subsequent signal processing at the greater sampling frequency, a decimation process is applied to the bit stream whereby a digital output signal at a rate of about the Nyquest frequency and with a desired relatively fine resolution is provided. Generally, the sigma delta modulator provides lower distortion and lower cost when compared to conventional converters.
FIG. 1 shows a model of a generic sigma delta modulator. The sigma delta modulator is shown in a discrete time domain (Z-domain) implementation where x(n) and y(n) are an input signal and an output signal, respectively, with signal values at discrete time instances n. The modulator comprises an input filter, G(z), a quantizer, Q, a loop filter, H(z), and an adder, S1, which calculates the sum of values input to it according to the shown signs i.e. values from H(z) is subtracted from values from G(z). It should be noted that other equivalent configurations exist e.g. where H(z) is arranged between the adder and quantizer or where H(z) is partitioned with an a-part between the adder and the quantizer and a b-part in the feedback loop.
For a low-pass sigma delta modulator, the feed-back loop of the sigma delta converter acts as an integrator, which in combination with the adder S1 ensures that the quantization error in average is zero or close to zero. The sigma delta modulator acts as a low-pass filter for an input signal and as a high-pass filter for the quantization noise. This is an expedient behaviour in that, when the loop filter is designed to pass input signals in a band of interest, quantization noise is attenuated in that band of interest band.
The noise attenuation is appreciable even with a first-order sigma delta modulator, that is, a modulator comprising a single integrator stage upstream of the quantizer, but to achieve the required high signal/noise ratios of high resolution converters, it is necessary to use higher-order modulators, that is, modulators comprising several integrators in cascade. However, if a higher-order modulator is used, stability problems arise.
In the design of the sigma delta converter it is an objective to minimize the quantization noise in the pass-band produced by the quantizer Q, i.e. to modulate the quantization noise. Further it is a objective to maximize the signal swing of the modulator output in the signal band of interest or the filtered modulator output signal (usually called MSA) and the goal is to achieve an MSA as close to one 1.0. The MSA is especially important for modulators with 2, 3, 4 levels quantizer Q(z) (or low levels quantizer), since the normal S-domain/Z domain stability criterions do not apply for this highly nonlinear system.
Both of these objectives will maximize the dynamic range of the modulator and the last objective are especially useful in Class D converters and in low voltage implementation of the modulator. A Third objective is to minimize the die size, which will reduce cost and power consumption of the modulator in an ASIC implementation.
In order to reach the third objective of minimizing the power/die size in an ASIC design of the modulator it is crucial to use 1 bit or low number quantization levels. Low number of levels in the quantizer of the modulators generates more quantization noise in order to attenuate the quantization noise in the signal band it is necessary to use high order and very aggressive feedback loops filters H(z) with a Noise Transfer function (see definition later) that has a very steep transition between stop/pass band and high attenuation in the stop-band. Again, a high order aggressive feedback loop filter will lower the MSA. If the MSA is very low, the Noise Transfer Function of the modulator would have a very good attenuation of the quantization noise, but since the MSA is low it will jeopardize the dynamic range and full scale signal swing. In order to optimize the dynamic range/SNR of the modulator there exists an optimum choice of MSA.
Unfortunately these above three objectives are partly conflicting, and a compromise has to be made i.e. a trade off exists between minimizing the quantization noise (in the pass-band) and obtaining high MSA and so on. Usually the optimum, taking all three objective into consideration, ends up with an MSA around 0.5 (or 6 dB below full-scale). See for example the DSD1702 data sheet from Texas Instruments where a sigma delta modulator is used in a D/A converter.